The standard deviation is defined as the average amount by which individual data items in a data set differ from the arithmetic mean of all the data in the set.
The standard deviation is the square root of the variance. It is denoted by the symbol .

More About Standard Deviation

If a set of data has n values and if represents the mean of the data set, then the standard deviation is given by:

Video Examples: What is a "Standard Deviation?" and where does that formula come from

Example of Standard Deviation

If electricity bills (in dollars) of 8 houses are 70, 82, 76, 79, 83, 85, 72, 77 and mean is 78 then find the standard deviation.
Standard deviation

Solved Example on Standard Deviation

Ques: A survey conducted by an automobile company showed the number of cars per household and the corresponding probabilities. Find the standard deviation.

Choices:

A. 4.24
B. 0.63
C. 0.79
D. 1.9
Correct Answer: C

Solution:

Step 1: Representing the data in the table and compute X .P(X) and X2 . P(X)

Step 2: From the table, we get
Step 3:
Step 4: Variance
Step 5: Variance
Step 6: Standard deviation
Step 7: So, the standard deviation is 0.79.